Search results for tag #math
hello world! I'm a #queer programmer living the #cyberpunk life in berlin.
I spend my time with #linux, #math and #rust, which often leaks into #elitedangerous and #satisfactory.
when I'm not at the keyboard, I'm reading, playing #dnd or watching #startrek.
most of my soundtrack is #metal, except when it's #eurovision.
#trans rights are human rights. if you have a problem with this, just fuck off please.
and society still is all about class struggle. #workersunite!
that's my #introduction
📺 https://peer.adalta.social/w/mjzW4Y2EoQBG3rxJRM8U5h
🔗 [🇩🇪🇺🇸🇫🇷](https://adalta.info/articles/prstn_who_116330456243696530_fr)
🔗 [ℹ️](https://numbword.com/")
Une énigme mathématique parfaite, révélant des schémas de résolution complexes.
📺 https://peer.adalta.social/w/6YAvi6rv1bkeHqpeDJTWRb
🔗 [🇩🇪🇺🇸🇫🇷](https://adalta.info/articles/prstn_who_116330456243696530_en)
🔗 [ℹ️](https://numbword.com/")
A Perfect Solution Reveals a Fundamental Flaw in the Game’s Design.
📺 https://peer.adalta.social/w/58mBZLC7KXoTXd8eFNADs2
🔗 [🇩🇪🇺🇸🇫🇷](https://adalta.info/articles/prstn_who_116330456243696530_de)
🔗 [ℹ️](https://numbword.com/")
Die Lösung: Eine ungewöhnliche Zahlenfolge und ihre sprachliche Entsprechung.
The futility of rushing too fast
Structurally it appear s very similar to the question off why buses often appear in threes’ and the stop go effect of red lights.
Having sat with the notion for about six months now, I think Jay's critique of the Church-Turing thesis has legs. I don't see clearly yet exactly where and how the limits of computation manifest in his own system(s), which of course they must. But I think he's correct that this thesis as it's colloquially presented (and taught to students, including me!) is misleading at best and false in a certain important sense. Apparently he is regularly called a crackpot for forwarding this critique even though it's straightforwardly demonstrated.
Waaldijk's book is more of a constructive mathematics exploration. In this it is closely related to computer science, but it's focused on traditionally mathematical notions like topological space. The latter is usually quite complicated, but Waaldijk shows that the core concept of compact space can be represented with finitely-branching trees, making these spaces amenable to computation. Since we imagine physics taking place in spaces that are topological (among other things) there's potentially an interesting bidirectional flow of ideas between computer science and physics.
Jay calls his central notion "natural trees". Waaldijk calls his central notion "natural spaces". In both cases I think the intended sense is "with minimal artifice".
✨🪲 Researchers are studying the mathematical models that allow thousands of #fireflies to blink in perfect unison.
By observing these bioluminescent #insects, scientists can better understand how decentralized systems coordinate complex behaviors without a single leader.
👉 https://arstechnica.com/science/2026/03/the-science-of-how-fireflies-stay-in-sync/
#biology #physics #nature #science #wildlife #entomology #math #bioluminesence
Astronomers have discovered 11 more moons around Saturn, bringing its total to 285--by far the most of any planet in the solar system.
The true number may be unknowable, if you count every ring particle as its own little moon.
https://minorplanetcenter.net/mpec/K26/K26F14.html #space #science #nature #math
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In the upper half of the illustration, the 21 largest Saturn satellites are represented full-scale with respect to each other and in relation to the parent planet (beige circular segment under the moons) and to the rings (in the background). The lower half shows the positions of several of the moons up to a distance of approximately seven Saturn radii from the planet's centre, which can be seen as an outline hemisphere having a radius of 71,500 kilometres at the left (shown in correct full scale).
Weekend project: my kid needed a tool to visualize math concepts, so I coded one. The power of vibe coding. Actually the power of professional vibe coding 😊 #vibecoding #math #professionalVibeCoding
They teach you the "English system" on antenna calculations in the US.
468 / Frequency = half wave dipole in feet
Then multiple by 12 for inches, divide by two for each side blah blah blah
In meters, 142.5 / Frequency = half wave dipole... but it corresponds to the band names.
In meters, for a 10 meter dipole at 28.500... you need an antenna that is 5.000 meters (half wave of 10 meters). 🙄 That's WAY EASIER.
20 meters at 14.250Mhz? 14.250/142.5 = 10 meter half wave dipole.
A lab mate shared this write up of Don Knuth using LLMs to solve a math problem: https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
It's clear that using Claude did help them arrive at some new understanding here, which is wonderful. I'm happy for them.
However, I'm upset by how much they personify Claude and attribute the solution to "him."
From this narrative, it's clear that the humans were very actively involved from beginning to end. Claude was a helpful tool, but it did not solve this problem on its own. What role did it actually play? How was it like or unlike a human collaborator on this problem?
It did generate a crucial insight, but where did that come from? Was it plagiarized from some unknown source? Did it "just emerge" from text completion and interpolation in latent space? Do we need some other explanation for Claude's apparent creativity?
These folks don't care. They just wanted a solution, which they attribute to Claude, and leave it at that. I think that's a serious problem.
#math #economy #cantaloupes #whatTheHell
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Charles M Schulz PEANUTS cartoon of Sally at school looking at a sheet of paper saying "ONLY IN MATH PROBLEMS CAN YOU BUY 60 CANTALOUPES AND NO ONE ASKS WHAT THE HELL IS WRONG WITH YOU"
Ooof, this smells of a sign/math error somewhere, ouch.
"...the software that should have pointed Lunar Trailblazer’s solar panels toward the Sun instead pointed them 180 degrees away from the Sun...."
Hands down the coolest website I've seen recently!
People calculated the longest (human) lines of sight for any point on earth!
https://map.alltheviews.world/longest/-127.77009398744215_50.17687825913197
#Maps #Mountains #Science #Math #Hiking #Dreams
Is it just me, or isn't it incredibly weird that all the USB powerbanks and lots of mobile device batteries use the unit mAh ... and then values like 20 000 or 5 000.
20 000mAh is the same as 20Ah.
#jouRapNal #book18 day 75
20260226Thu
#3goodThings #couch #volunteer #french #threeGoodThings
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(illustration of a couch)
iL is picking up Yt after volunteering and tells me i may have to couch surf or be homeless
Az sent me a Tik Tok where my name was sung
Ma is back to hs with a makeup quiz & some french verb conjugations
One of my greatest learning laments were my failed attempts at Calculus in high school and post college. By the time I got to Calculus in high school I was so burnt out, and had a terrible math teacher the year prior that one of my favorite academic interests had suffered a grievous wound.
I attempted a college Calculus course after I attained my Bachelor's degree. Leading up that attempt I took trigonometry course by correspondence and a pre-calculus course both of which I excelled at.
Got into the Calculus course then life started lifing and I was unable to complete it.
All this to say, I still want to know Calculus, even if I never use it outside of learning it.
#music #math #algebra #earworms
'Behind many great melodies, researchers found something surprisingly powerful: symmetry. Their work shows that advanced algebra can reveal deep musical patterns that are not always obvious by ear or even on a written score.'
https://uwaterloo.ca/news/media/secret-math-behind-catchy-melodies
Mathstodon.xyz is a Mastodon server for people who love maths, and includes LaTeX rendering in the web interface. Maths chat is especially welcome, but any topic of conversation following the code of conduct is OK.
This server has a post size of up to 1729 characters.
You can find out more at https://mathstodon.xyz/about or contact the admin account @christianp
#FeaturedServer #Mathematics #Maths #Math #Mastodon #Fediverse #FreeFediverse
Name suffixes - a mark of the patriarchy.
This is a summary table of a registered voter list for a county in New Mexico (United States). The occurrence count of various name suffixes is further broken down by gender.
I have no idea how this may compare to name suffixes in other countries, other cultures.
This is not a scientific study. There are all sorts of problems, such as selection bias.
But the difference in occurrence between men and women is huge.
#Patriarchy #Feminism #Data #Math #Culture #GenderEquality #Statistics
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A summary table that shows various name suffixes (2nd, 4th, SR, etc.) that is further broken down by gender. The difference in occurrence between men and women is huge.
Took Algebra at a local community college and had to work really hard to get an 'A-'. Credit did not transfer to my university, so had to take algebra again (I think I got a 'B' but the teacher was much worse than the one at the community college.
Now, one of my sons is learning trigonometry by taking a C programming course from Pikuma... and he's interested in it.
https://pikuma.com/courses/learn-3d-computer-graphics-programming
#math
RT: https://poa.st/objects/60e46c4f-82ce-4554-bd0a-585b162786d6
Happy birthday to #mathematician Johann Peter Gustav Lejeune Dirichlet (13 February 1805 – 5 May 1859)! My lino block print illustrates the famous mathematical tool known as the pigeonhole principle, which states that if n items are put into m containers, with n > m, then at least one container must contain more than one item. You can imagine a bunch, call it m, pigeonholes and n pigeons, where n > m; 🧵
https://minouette.etsy.com/listing/1297260728
#linocut #printmaking #sciart #mathart #mastoArt #math #histsci
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My linocut print of the Pigeonhole Principle shows Dirichlet in blue, a bearded man with heavy brow, wearing a suit with arms crossed, looking a bit cross. Behind him is a bank of pigeonholes in a gradient of blue to gold. Each one contains one or two pigeons in black on grey with turquoise and violet markings. The pigeonholes may extend infinitely in all directions - the shelves appear to go on beyond the 4 x 7 array of pigeonholes shown.
What is a number? When you think of the concept, what do think of? Answer in the poll!
In your conception, is this kind of number fundamental, or do you feel that it relies on something more fundamental? If so, is that simply a standard construction (like the rationals from the integers) or something different?
#math #maths #mathematics
| A natural number: | 0 |
| An integer: | 0 |
| A rational number: | 0 |
| A computable number: | 0 |
| A real number: | 0 |
| An ordinal or cardinal number: | 0 |
| Something else?: | 0 |
Mathematicians discover new ways to make round shapes
https://www.scientificamerican.com/article/mathematicians-discover-new-ways-to-make-round-shapes/
Math people, looking for ideas/recommendations. I have this teen who loves math. Super smart. Loves geometry. Loves number-theory-ish things. 3d thinker; really into engineering/design sorts of things - 3d print, crafting with all sorts of materials. Also musical; plays a few instruments.
She wants to work on some or another piece of math with me, outside of school. I am looking for a good project, book, or set of materials to start working through together. I would love recommendations.
For example, are there suitable and engaging materials, or a book, we might work on together re: analytic number theory, or complex analysis, or even some music & math or math & engineering materials...? She doesn't know calc yet, but would be good to learn along the way as long as it's not jumping too deep, too quickly.
There is much truth to this post about about #math textbooks.
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Screenshot of a post by cauchys-special-boy:
if there's one thing ive learned from my math education it's the ability to judge a textbook by it's cover:
fancy cover with actual picture, fewer than 15 years old, $300: absolute dogshit. time wasting exercises, poor exposition, that weird gloss they put on the pages probably makes it too toxic to use as kindling
title is just name of subject, referred to by author, 50 years old with like 3 editions: excellent. compact proofs, exercises good enough people refer to them by number in conversation. available for free by foraging somewhere they grow naturally
title is some shit like paul's notes, "cover" is just default latex titlepage, distributed as pdf to grad classes or by advisor: best coverage of whatever (usually niche) topic it's about in the world. crystal clear exposition. solutions to exercises available by emailing grad students working under author
Know why cats are good at math? It is because they study and practice in their daily lives.
#math #caturday #caturdayeveryday
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a cat studying a math book with a chapter in fractions
🌎📐 Working at the Naval Proving Ground in #Virginia, Dr. Gladys West used complex algorithms to map the #Earth’s irregular "geoid" shape.
Her mathematical foundation, combined with #Einstein’s relativity, is what allows the #GPS on your phone to be accurate within centimeters today.
👉 https://bigthink.com/starts-with-a-bang/gladys-west-einstein-gps/
#math #stem #blackhistory #physics #history #technology #innovation
Vulcan | The Planet That Didn't Exist
https://www.youtube.com/watch?v=iJyweEcpsGc
Re-watching one of my favorite #youtube #documentaries. It is a nice #historical approach to how #sicence is constantly working to improve and challenge it self.
#relativity #astronomy #documentary #mathematics #physics #math #stem #history #historyofscience
This reminds me of: Dialogue Concerning the Two Chief World Systems
Dialogue Concerning the Two Chief World Systems (Dialogo sopra i due massimi sistemi del mondo) is a 1632 book by Galileo Galilei comparing Nicolaus Copernicus's heliocentric system model with Ptolemy's geocentric model. Written in Italian, it was translated into Latin as Systema cosmicum[1] (Cosmic System) in 1635 by Matthias Bernegger.[2] The book was dedicated to Galileo's patron, Ferdinando II de' Medici, Grand Duke of Tuscany, who received the first printed copy on February 22, 1632.[3] It consists of four Socratic dialogues between the Copernican Salviati, the educated layman Sagredo and the geocentrist Simplicio. They discuss the findings of their "mutual friend the Academician" (Galileo).
https://en.wikipedia.org/wiki/Dialogue_Concerning_the_Two_Chief_World_Systems
How can drugs get more expensive? He already brought down their prices "600%, 700%, 1000%".
The 500k-ton typo: Why data center copper math doesn't add up
#HackerNews #dataCenterCopper #typo #math #investing #news #technology
Mesopotamian pottery from 8,000 years ago may indicate mathematical thinking. I was told there would be no math
The glider now has 12 pounds of lead shot and epoxy added to dead space in the very end of the tail boom.
My initial estimate of volume indicated that I could add 8 - 10 pounds this way. I'm pleasantly surprised, and I didn't make a chocolate covered mess of things as I was pouring this goop into the tail.
I need to add a few more pounds to the tail. Phase two of this project will use lead plate, bolted to the vertical fin spar. (I need to unroll the 1/4-inch plate first, then develop a template to cut the lead.)
I could not add the epoxy/lead shot mix all at once because of the exothermic reaction of epoxy. When mixed epoxy is in a thick blob (instead of a thin layer), it generates enough heat to warm itself...which accelerates the chemical reaction...releasing more heat...further accelerating the reaction.... I have seen epoxy smoking hot because of this, so I added a bit, waited a half hour, checked temperature with an IR non-contact thermometer, added a bit more when it was clear that the exotherm was only very mild, etc. That took a while, but turned out well.
I note that Roto Metals has a discount on some 1-inch lead plate. Get your fork lift ready. No free shipping!
https://www.rotometals.com/lead-sheet-plates/sheet-lead-1-64-lbs-sq-ft/
#AvGeek #Aviation #ElectricAircraft #Homebuilt #Glider #DIY #EAA #Ballast #Math #Density #Exothermic #Chemistry #Thermodynamics #Lead #Epoxy
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A view from inside the tail boom, aft of the tailwheel, looking aft. A Plexiglass dam was caulked into place as a 'dam' to hold the lead shot and epoxy mix. I was able to fill up to the dam, then top off with extra epoxy. The lead shot is dark gray and most of the tail boom interior is carbon fiber...black.
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A view of the very end of the tail boom, looking forward. Two dams on the sides of the tail boom's circular cross section are holding back several pounds of lead shot and epoxy. The ends of the rudder cables are wrapped in blue tape to keep away epoxy.
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Dark gray lead sheet, 1/4-inch thick, needs to be unrolled and then cut into rectangular sections and bolted into the tail for further ballast.
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Do you need any 1-inch thick lead plate? Cheap at the price! No free shipping!
https://www.rotometals.com/lead-sheet-plates/sheet-lead-1-64-lbs-sq-ft/
I need some #math / #machinelearning / #AI / #physics people to confirm for me that the topology of latent space shows non-Euclidean characteristics. This is not for a technical project; I'm trying to understand just how well cultural theorists are using their mathy metaphors. Thanks in advance!
If you were writing a bignum library in C what would you call it?
This is a quasi-serious question.
The working name is “Rx” for internal reasons. I’ll stick with that if I can’t get something better.
Time for a new #introduction!
I live on the border, where #Arizona, #Mexico and #NewMexico all come together.
I mostly post about #cooking, #gardening, #hiking and #publiclands
I'm interested in #music, #art, #anime, #manga, #comics, #math, #videogames, #retrogaming and #retrocomputing
I switched from #Amiga to #linux and #bsd so I actually know very little about MS Windows.
One of the selling points touted for Synergy Aircraft was the ability to fly in and out of small airports all across the United States. This particular aircraft design has a fairly long range and a fairly fast cruise speed.
In recent years development of this project has slowed, and top leadership has been replaced. I do not know many details about current status.
The aerodynamic refinements used in this design interest me.
String Theory Inspires a Brilliant, Baffling New Math Proof
Years ago, an audacious Fields medalist outlined a sweeping program that, he claimed, could be used to resolve a major problem in algebraic geometry. Other mathematicians had their doubts. Now he says he has a proof.
https://www.quantamagazine.org/string-theory-inspires-a-brilliant-baffling-new-math-proof-20251212/
Boys do math problems like this: *weird walk*. Girls do math problems like this: *weirder walk*
Atmospheric refraction, due to the different temperature/altitude profile in the atmosphere at different times of day...makes distant mountains appear taller or shorter.
The attached photo is a comparison of what I shot yesterday afternoon and this morning. The camera was set up within inches of the same location for both shots, and those mountains are between 50 and 120 miles away...so I'm saying that any parallax effect from camera location is essentially zero.
I have annotated with arrows where it's easy to make a comparison of how the near and far ridge lines overlap differently in the two photos.
This is a follow up to:
https://universeodon.com/@KrajciTom/115673789231444526
Imagine the care that was needed to conduct surveys before the GPS/GNSS era:
https://explorersweb.com/the-five-men-who-measured-mount-everest/
"The Great Theodolite built by Troughton & Simms in London stood nearly 1.5m high, had a horizontal circle one meter in diameter, and could read angles to a single second of arc. Moving it required 30 porters and sometimes elephants."
"The reduction of Nicolson’s observations was a colossal task. Each ray from each station had to be corrected for instrumental error, for temperature and pressure, and for the curvature of the Earth. Above all, they needed to correct for atmospheric refraction, which at those distances could amount to six or seven minutes of arc and change from hour to hour."
#Atmosphere #Refraction #Physics #Math #GIS #Datum #Survey #Geodetic #Map #Optics #Science #Parallax #Cool #NewMexico #Theodolite
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A comparison of two photos of the same distant mountain ridges. Arrows show places where the ridgelines overlap in different ways in the two photos. The top photo is grayscale, the bottom one is color.
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The great theodolite. Photo: Survey of India Archives
I have a #math question. Everyone inclined to snicker, please look away.
I need to take the integral of (e^x)*(sin^2(x))*(cos(x)) (and variants thereof). I don't think I can simplify this anymore so I can get this into, basically, a function of two terms.
Does it make sense to find the integral of (sin^2(x))*(cos(x)) and then use that information to integrate the whole function by parts, with (e^x)dx being the other "part"? It's been days and I can't think of any other way to do this.
TIA!
One thing I like about this book is its approach to eigenvalues and eigenvectors. Most linear algebra books present eigenvalues as roots of the "characteristic polynomial", which is built from the "determinant", which in turn has some formula defining it. These objects are rarely motivated geometrically, and so you're left with limited understanding of just what an eigenvalue is or why linear transformations on finite-dimensional vector spaces must have them. Axler avoids determinants till Chapter 9 of the book, focusing instead on linear operators. The fact that operators must have eigenvalues pops out of the observation that iterating an operator on a given non-zero starting vector results in a set of vectors that must eventually become linearly dependent. This fact also leads to the development of the characteristic polynomial; you can then come at the determinant from this, more geometric, perspective.
Here's one. If you're given a function, you can treat argmax of that function as a set-valued function varying over all subsets of its domain, returning a subset--the argmaxima let's call them--of each subset. argmax x∈S f(x) is a subset of S, for any S that is a subset of the function f's domain. Another way to think of this is that argmax induces a 2-way partitioning of any such input set S into those elements that are in the argmax, and those that are not.
Now imagine you have some way of splitting any subset of some given set into two pieces, one piece containing the "preferred" elements and the other piece the rest, separating the chaff from the wheat if you will. It turns out that in a large variety of cases, given only a partitioning scheme like this, you can find a function for which the partitioning is argmax of that function. In fact you can say more: you can find a function whose codomain is (a subset of) some n-dimensional Euclidean space. You might have to relax the definition of argmax slightly (but not fatally) to make this work, but you frequently can (1). It's not obvious this should be true, because the partitioning scheme you started with could be anything at all (as long as it's deterministic--that bit's important). That's one thing that's interesting about this observation.
Another, deeper reason this is interesting (to me) is that it connects two concepts that superficially look different, one being "local" and the other "global". This notion of partitioning subsets into preferred/not preferred pieces is sometimes called a "solution concept"; the notion shows up in game theory, but is more general than that. You can think of it as a local way of identifying what's good: if you have a solution concept, then given a set of things, you're able to say which are good, regardless of the status of other things you can't see (because they're not in the set you're considering). On the other hand, the notion of argmax of a function is global in nature: the function is globally defined, over its entire domain, and the argmax of it tells you the (arg)maxima over the entire domain.
In evolutionary computation and artificial life, which is where I'm coming from, such a function is often called an "objective" (or "multiobjective") function, sometimes a "fitness" function. One of the provocative conclusions of what I've said above for these fields is that as soon as you have a deterministic way of discerning "good" from "bad" stuff--aka a solution concept--you automatically have globally-defined objectives. They might be unintelligible, difficult to find, or not very interesting or useful for whatever you're doing, but they are there nevertheless: the math says so. The reason this is provocative is that every few years in the evolutionary computation or artificial life literature there pops up some new variation of "fitnessless" or "objective-free" algorithms that claim to find good stuff of one sort of another without the need to define objective function(s), and/or without the need to explicitly climb them (2). The result I'm alluding to here strongly suggests that this way of thinking lacks a certain incisiveness: if your algorithm has a deterministic solution concept, and the algorithm is finding good stuff according to that solution concept, then it absolutely is ascending objectives. It's just that you've chosen to ignore them (3).
Anyway, returning to our friend argmax, it looks like it has a kind of inverse: given only the "behavior" of argmax of a function f over a set of subsets, you're often able to derive a function g that would lead to that same behavior. In general g will not be the same as f, but it will be a sibling of sorts. In other words there's an adjoint functor or something of that flavor hiding here! This is almost surely not a novel observation, but I can say that in all my years of math and computer science classes I never learned this. Maybe I slept through that lecture!
#ComputerScience #math #argmax #SolutionConcepts #CoevolutionaryAlgorithms #CooptimizationAlgorithms #optimization #EvolutionaryComputation #EvolutionaryAlgorithms #GeneticAlgorithms #ArtificialLife #InformativeDimensions
(1) If you're familiar with my work on this stuff then the succinct statement is: partial order decomposition of the weak preference order induced by the solution concept, when possible, yields an embedding of weak preference into ℝ^n for some finite natural number n; the desired function can be read off from this (the proofs about when the solution concept coincides with argmax of this function have some subtleties but aren't especially deep or hard). I skipped this detail, but there's also a "more local" version of this observation, where the domain of applicability of weak preference is itself restricted to a subset, and the objectives found are restricted to that subdomain rather than fully global.
(2) The latest iteration of "open-endedness" has this quality; other variants include "novelty search" and "complexification".
(3) Which is fair of course--maybe these mystery objectives legitimately don't matter to whatever you're trying to accomplish. But in the interest of making progress at the level of ideas, I think it's important to be precise about one's commitments and premises, and to be aware of what constitutes an impossible premise.
There’s a fine line between a numerator and a denominator.
Only a fraction of people will find this funny.
Say you have a notion of "context", and a way of ordering these so that some contexts are larger, more expansive than, or "above" others. And let's say in each context, there is a set of things that are identifiable as "best". I'm being vague because you can instantiate this basic idea pretty broadly. For instance, maybe the contexts are states of information in a search algorithm and "best" refers to the possible solutions that seem best in each state of information; as you search, you change (increase) your state of information, and might change your might about which possible solutions are the best one. As another example, the contexts could be possible worlds and "best" refers to which propositions are true in each possible world; as you progress from one possible world to the next, you might change your mind about what propositions are true.
Anyway, with that simple setup you can associate to each thing the set of all contexts in which it appears best. This set could be empty or could be very large or anything in between. Then the lower order shows up as a weak preference relationship among all the things: one thing is lower preference than another if, for each context in which it appears best, there's a larger or equal context in which the other thing seems best. Put differently, any time you think the first thing is best, there's a way to increase your context such that the other thing appears best. This is exactly the lower order between the sets of contexts in which each thing seems best. If the set of contexts in which one thing seems best is higher up the lower order (😝) than the set of contexts in which the other seems best, then the former thing is weakly preferred to the latter.
The intuition in a search setting is that contexts are states of information, a kind of compendium of what you've learned so far in your search. If x and y are possible solutions, and for every context (state of information) in which you think x is the best there is always a bigger context--i.e., with more information--in which you think y is best instead, you ought to prefer y to x. The rationale is that any time you think x is best there's a way to learn a little more and change your mind to think y is best instead, which justifies preferring y to x.
Applied to modal logic, this notion corresponds to validity: if in every possible world where the proposition p is true there is an accessible world in which proposition q is true, then "p implies possibly q" is true in every world (valid).
The appearance of "possibly" is suggestive I think, and concords with this being a weak preference. "Necessarily" would be a strong preference, but I'd expect (in the sense of demand) a search process follow such a preference directly.
#math #ComputerScience #search #CoevolutionaryAlgorithm #SolutionConcept #ModalLogic
#SlowScience #math #CoevolutionaryAlgorithm #SolutionConcept
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Picture of a blackboard with some math scribbled on it. Below in the foreground there's a computer screen with some of the math typeset. I'm happy to describe to math to anyone who's interested but I'm not going to attempt to put a more detailed description here.
But the American Ornithological Society is making an effort with respect to bird names, and working through the controversies: https://americanornithology.org/english-bird-names/aos-pilot-project-to-change-harmful-english-common-bird-names/
and I think all of science and math can and should follow their lead. The world doesn't need "McCown's longspur" (McCown being a Confederate general complicit in genocide), and we don't need, for example, anything named after people like Gentzen either if you ask me: "In April 1939 Gentzen swore the oath of loyalty to Adolf Hitler as part of his academic appointment"; "Under a contract from the SS, Gentzen worked for the V-2 project" (from https://en.wikipedia.org/wiki/Gerhard_Gentzen)
Science results and math theorems should not be named after people, and we should undertake to rename any that currently are. We should prioritize renaming results or theorems named after white men and other privileged categories of people, with special attention to cases where a privileged person accepted or was assigned credit for work a less-privileged person did.